Oxygen-disorder and correlation effects on the hole concentration and metal-nonmetal transition in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$

A detailed analysis of the effect that oxygen disorder has on the electronic structure of the highly correlated high-${\mathit{T}}_{\mathit{c}}$ superconductors is presented. The system is modeled by a Hubbard-type Hamiltonian in which the on-site and intersite correlations between oxygen and copper atoms are included. The Green-function formalism is used to calculate the local electronic density of states at the Cu and O sites characteristic of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{6+\mathit{x}}$ as a function of oxygen concentration x and of the cation charge Q. Due to the large electronic interactions, a Mott-Anderson metal-nonmetal transition is obtained, in accordance with the experimental findings. The hole concentration n is calculated for disordered and ordered systems. A plateau in the concentration dependence of n is obtained for 0.45≤x≤0.75, only in the ordered system. The correlation functions of the various charge states in Cu and O are also calculated and discussed.